Step 5: Get it cut.

Next cut rectangle piece of plastic.
Sand face and back sides of plastic plate with fine sandpaper to diffuse light then cut notches on sides of plate where you plan to install LEDs.
Shape of LED should be formed with file to fit into the notch

Step 6: Let's practice some LEGO ;-)

Something like that.
You can use hot glue to secure it on place.

Step 7: Let's give it a trial...

Not bad for me ;-)

Step 8: Bring all bunnies into the cage.

Now everything is ready to be assembled:
-PCB;
-white sheet of paper to reflect light back;
-polarizing filter (if you removed it by mistake);
-plastic plate with embedded LEDs;
-glass assembly;
-frame.

NOTE:
Be very careful with golden pads on PCB and elastomer connector (zebra strip). Use pure alcohol to clean it if you touched contact pads with your fingers.
Another important thing is proper alignment.
If after powering it up you got missing lines (characters) on LCD then connector has shifted from original position. Carefully take it apart and re-align it.

Step 9: Final step.

I hope you already calculated value of resistors you need.
So, solder it up.
There are two points to get power to LED from.
You can connect it directly to logic power supply (pin 0 - GND, pin 1 - 5V) of LCD.
Or you can make separate connection(on my LCD there were unused pads for optional backlight) and in that case you'll be able to use PWM signal to control brightness of LED.

Step 10: One more example

I've used similar technique to modify antique analogue meter for my next project.

Another tip — If you wrap the edges of the plastic/plexiglass with shiny material (aluminum foil/tape) it will reflect the light back into the plastic and create a stronger, and more even, backlight. This was discovered after dissecting an LCD from my clock radio and seeing how they did it.

Just wondering if anyone in here had experience gluing a layer of glass on a LCD screen with UV glue? If so, I would love some advice on how to do this with little to no spill-over so that it doesn't get into the circuit board components that are around the edges of the LCD screen itself. I have heard there are issues with applying pressure to the LCD screen with anything heavier than just the glass itself so I was wondering how to calculate the right amount and placement of the UV glue if I cannot apply any pressure to spread it out....

Picture and text show polarizing filter below the plastic lighting plate (if you removed it by mistake). If the filter had not been removed it would be above the plastic lighting plate. What is the reason for this layering change or is this a typo?

Very Nice! I'll have to try this with my old GBA if I can muster the courage to meddle with it's guts... (and find it in the first place!) A thought for the analogue meter, if you replaced the Backlight LEDs with UV LEDs and then coated the needle in UV-reactive paint (or a mixture of glue and glow powder) then you'd easily be able to read the value even in the dark!

Not to quibble but the reason old analogue meters have the reflective strip is so that you can line up your eye with the needle and its reflection and thus avoid erroneous readings caused by the distance between the needle and the scale and the angle at which you look at it. Not that that always matters but I thought it might be an interesting titbit.

The word you are looking for is parallax: the apparent displacement or the difference in apparent direction of an object as seen from two different points not on a straight line with the object; (Merriam-Webster)

Not quite, although I could have used parallax in the description it would not do on its own and I was deliberately more liberal with words to make it clear anyway. So I wasn't really looking for the word parallax :)

I think it's possible but some research work is required. 1. Select white LEDs with proper optic characteristic. 2. Fit them into the room which is provided for a slim CCFL tube. 3. Give it long test run to check if eyes will feel good after several hours of staring at new screen. ;-)